Let A_{2} be the set of all multiples of 2 except for 2. Let A_{3} be the set

CoormaBak9

CoormaBak9

Answered question

2021-08-22

Let A2 be the set of all multiples of 2 except for 2. Let A3 be the set of all multiples of 3 except for 3. And so on, so that An is the set of all multiples of n except for n, for any n2. Describe (in words) the set A2A3A4

Answer & Explanation

Aamina Herring

Aamina Herring

Skilled2021-08-23Added 85 answers

Step 1
Given that A2 is the set of all multiples of 2 except for 2. In this set all the even numbers except 2 are covered.
Similarly, An is defined such that it is the set of all multiples of n except for n.
Now consider a composite number m.
Then m=ab with (a,b)=1
Then the number m belongs to the set Aa and Ab
Hence it belong to the set A1A2A3 And thus it cannot belong the set A1A2A3
Step 2
On the other hand, consider a prime number p.
Then it cannot be written as a multiple of any element other than p and 1.
By the definition of the set Ap, p does not belong to Ap
which gives that p belongs to A1A2A3
Finally, the set of all odd primes will constitute the set A1A2A3

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Discrete math

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?